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Nowak and Sigmund characterise the strategy space as: k ≤ 0 denotes coop-

eration, since agents will interact with most other agents, and k > 0 denotes

defection (also called selfish by Nowak and Sigmund). We further divide the

cooperative strategy space intounconditionally cooperative (−5≤k≤ −2) and

conditionally cooperative (−2 < k ≤ 0). We describe interaction choices as

follows. We refer to interactions in which an agent cooperated based on its

perceived image score of the recipient, when it should have defected based on

theactual image score, or vice-versa, as misclassified interactions. An interac-

tion is called incorrect cooperation if an agent cooperates when it should have

defected. Anincorrect defection is an interaction in which an agent defects (i.e.

does not donate to the recipient) when it should have cooperated. The num- ber of misclassified interactions is the sum of the incorrect cooperations and incorrect defections. Incorrect defections are undesirable since they reduce the donor’s image score, leading to fewer subsequent donations to the donor. Incor- rect cooperations are undesirable since they allow selfish agents to gain higher payoff, and become more likely to be reproduced.

The absolute value of an agent’s image score that is maintained (to allow calculation of misclassified interactions) includes any incorrect cooperations or defections that that agent has made — it is the result of an agent’s actual actions rather than how they should have acted given complete information. It should be noted that whether an interaction is labelled incorrect or not is based on a global view of the system (since it is determined by comparing an agent’s decision with what they would do based on perfect knowledge of their interaction partner), and that an individual cannot know whether their choice is “correct” or not based on their local view of the system.

3.3.5

Gossiping mechanism

Gossiping is an appealing solution to the problem of incomplete information, and can supplement direct observation of interactions to increase the availabil- ity of information regarding potential interaction partners. In this section, we describe how our simple gossip mechanism is incorporated into image scoring in order to test its efficacy in supporting image scoring and promoting cooperative behaviour.

Our simple gossip mechanism spreads perceived image scores as follows: each agent maintains a queue of received gossips, which are processed in a separate gossip phase. After an interaction, each observer starts a gossip with probability

ogp (observer gossip probability) by sending a gossip packet to a randomly

chosen neighbour. The probability of any given agent starting a gossip thus

depends both ono, the probability it is chosen as an observer, and onogp, the

probability that an observer starts a gossip. Each gossip packet contains the image score of the donor, as perceived by the gossip starter, the unique ID of the donor, the unique ID of the gossip starter, and a time to live (TTL).

EverygossipRate interactions, there is a gossip phase. Each agent in turn

updates their image score values for each agent that they have received gos-

sips about using some update rule, and propagates the gossip with T T Lt+1 =

T T Lt−1 to a single randomly chosen neighbour that does not yet have the

gossip. The process is repeated untilT T L= 0. It is assumed that an agent can

check if a neighbour has received a gossip already.

We propose four update rules that gossip receivers can use to incorporate received gossip information.

1. Aggregate Average (AA): The agent replaces its perceived image score

for agenti with the average of its previous perceived score foriand the

values contained in all the received gossips concerningi.

2. Average Replace (AR): The agent replaces its perceived image score for

concerningi.

3. Majority Replace (MR): The agent replaces its perceived image score for

agentiwith the median value contained in all received gossips concerning

i. As noted above, it is thought that this is approximately how humans

process gossip (Sommerfeldet al., 2008).

4. Most Recent (MRec): The agent replaces its perceived image score for i

with the most recent value received, through gossips, concerningi.

Agents have incomplete information regarding interaction partners because they are unable to observe every interaction that a partner has engaged in. By introducing gossiping, we aim to increase the amount of information available so that individuals can make more accurate decisions without having to increase the number of observations they make. In this way, gossiping supplements (and, in some cases, substitutes) direct observation of agent behaviour. As such, levels of incomplete information should fall and, subsequently, cooperative behaviour will increase.

3.4

Experimental Setup

We model two primary situations in which incomplete information may un- dermine the efficacy of reputation: (i) when there is a very low probability of having observed any interactions, such as when first entering a system, and (ii) when there is a very low probability of observing a complete set of interactions. We model the first situation using a low ratio of interaction rate to popula- tion size, and the second situation using a very high ratio of interaction rate

to population size. Nowak and Sigmund used parameters of n={20,50,100}

and m = {125,200,300,500,1000} (where n is the population size and m is

the number of interactions per timestep), which is sufficient for modelling the first situation but limited for the second. To investigate the latter, we simu-

m/n= 500). We useo= 0.1, µ= 0.001, b= 1, andc= 0.1, and unless otherwise

stated, we use an observer gossip probability ofogp= 1.0 andgossipRate= 1.

Since the diameter of the networks we generate in our simulations is typically less than 5 we use a TTL of 5. We performed a number of simulations scaling

the population ton= 1000 to allow us to test the effects of group size.

We situate agents on a variety of network structures. We replicate Nowak and Sigmund’s completely connected topology, and implement random (such

that each pair of nodes is connected with probability p), scale-free and small-

world synthetic networks1_{. Scale-free networks are generated using the Eppstein}

and Wang (2002) algorithm and small-world networks using Kleinberg’s gener- ation algorithm (2000). Additionally, we use 8 network samples created using Breadth-First Search (BFS) (see Appendix A and Chapter 6 for detailed dis- cussion of BFS) from the Enron email dataset and the arXiv general relativity

section collaboration network2 _{to corroborate our results on networks that are}

structurally closer to those found in the real world. We use BFS, and not other network sampling algorithms, since (i) although it is known to be biased towards high degree nodes, it accurately retains the local network structures within the

sample (Gjokaet al., 2010), and (ii) it is intended only to be used as a check for

generality of our results rather than a full investigation on real-world networks. Our investigation focused on two main metrics: the strategy distribution for the population and the number of misclassified interactions. The results given are averaged over 20 runs for each parameter configuration, giving a standard

deviation that ranges from 1–14%. We used t = 10000 generations of evolu-

tion. Due to the cyclic nature of strategies identified by Nowak and Sigmund, analysing results at an arbitrarily chosen generation (e.g. the final generation

of t = 10000) is unlikely to provide a representative view of the simulation.

Accordingly, we present results averaged over the course of the simulation. 1_{Generated using the Java Universal Network/Graph Framework} http://jung.sourceforge.net/